In (1), using the theory of group representations, Brauer studied groups of finite order g containing elements A of prime period p which commute only with their own powers Ai. If is a p-Sylow subgroup of , the normalizer can be generated by A and another element B such that1.1,where ϒ is a primitive root (mod p), and t and q are positive integers such
that1.2 tq = p − 1.
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